JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (02): 75-82.doi: 10.6040/j.issn.1671-9352.0.2014.342

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Wajsberg's form of MTL algebras with applications

KOU Hai-yan, WU Hong-bo   

  1. School of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, Shaanxi, China
  • Received:2014-07-25 Revised:2014-11-20 Online:2015-02-20 Published:2015-01-27

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Abstract: MTL algebra is an important basic logic algebra. Firstly, the classical algebras forms of NMTL algebra is given by taking Wajsberg's method and some parts of axioms of MTL logic system, and it is proved that NMTL algebra and MTL algebra have identical structure. Secondly, it is proved that an NMTL algebras L satisfying the condition: ∀x,y∈L, x→y=(y→0)→(x→0) is BR0 algebra. Finally, it is proved that IMTL algebra and BR0 algebra have identical structure and the Wajsberg forms of BR0 algebra and BL algebra are given.

Key words: fuzzy logic, residuated lattice, NMTL algebra, BR0 algebra, BL algebra, MTL algebra

CLC Number: 

  • O141.1
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